Deep mines has 43,800 shares of common stock outstanding with a beta of 1.54 and a market price of $51 a share. there are 10,000 shares of 7 percent preferred stock outstanding with a stated value of $100 per share and a market value of $83 a share. the 8 percent semiannual bonds have a face value of $1,000 and are selling at 96 percent of par. there are 5,000 bonds outstanding that mature in 13 years. the market risk premium is 7.5 percent, t-bills are yielding 3.6 percent, and the tax rate is 21 percent. what discount rate should the firm apply to a new project's cash flows if the project has the same risk as the company's typical project?

Solution:

MV of equity=Price of equity*number of shares outstanding

MV of equity=51*43800

                    =2233800

MV of Bond=Par value*bonds outstanding*%age of par

MV of Bond=1000*5000*0.96

                   =4800000

MV of Preferred equity=Price*number of shares outstanding

MV of Preferred equity=83*10000

                                    =830000

MV of firm = MV of Equity + MV of Bond+ MV of Preferred equity

                 =2233800+4800000+830000

                 =7863800

Weight of equity = MV of Equity/MV of firm

Weight of equity = 2233800/7863800

W(E)=0.2841

Weight of debt = MV of Bond/MV of firm

Weight of debt = 4800000/7863800

W(D)=0.6104

Weight of preferred equity = MV of preferred equity/MV of firm

Weight of preferred equity = 830000/7863800

W(PE)=0.1055

Cost of equity

As per CAPM  , Cost of equity = risk-free rate + beta * (Market risk premium)

                       Cost of equity % = 3.6 + 1.54 * (7.5)

                       Cost of equity % = 15.15

Cost of debt

                K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

                  k=1

                 K =13x2

960 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^13x2

                  k=1

YTM = 8.5146699304

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 8.5146699304*(1-0.21)

                                   = 6.726589245016

cost of preferred equity

cost of preferred equity = Preferred dividend/price*100

cost of preferred equity = 7/(83)*100

                                       =8.43

WACC=after tax cost of debt*W(D)+cost of equity*W(E)+Cost of preferred equity*W(PE)

WACC=6.73*0.6104+15.15*0.2841+8.43*0.1055

WACC =9.3%